Cabinet Ministers rallied to the support of John Prescott yesterday as the list of colleagues jockeying to succeed him as deputy Labour leader continued to grow.

Commons leader Jack Straw is the latest name being put in the frame, reportedly with the backing of Downing Street, to join any fight for the elected position.

The development added to speculation sparked by Education Secretary Alan Johnson's public declaration that he would like to be the next in the job.

But Peter Hain, one of those widely tipped as a potential candidate, said he was a "strong supporter" of Mr Prescott and did not want him to quit immediately.

The Deputy Prime Minister faced calls to step down amid a row over keeping full pay and perks despite losing his department in Tony Blair's reshuffle. That followed revelations of his affair with diary secretary Tracey Temple.

Mr Prescott, on a tour of the US and Canada to promote the fight against climate change, gave up his grace-and-favour Dorneywood residence in a bid to end the furore.

But his bid to shift the spotlight from "daft" questions about his future to policy issues has failed to quell suggestions that the race to succeed him has already begun.

In a recorded interview broadcast yesterday morning, Mr Johnson said that while he would not campaign while Mr Prescott was in the job, it was a role he would like to take on.

His comments were seized on by backbencher Ian Davidson, who said it meant "the starting gun in the leadership and deputy leadership election has already been fired".

Mr Hain refused to be drawn on whether he had been approached by trade union leaders to contest the deputy leadership, insisting: "There is no vacancy."

He said: "I am a strong supporter of John Prescott.

"I think he does a very good job and I hope he'll continue to do that job and let's get down to the issues that really matter to people."

Party members were "frustrated and irritated" by the speculation, he said, and wanted the Cabinet and others to "get on with the job".

He appeared to back suggestions that Mr Prescott could depart at the same time as Mr Blair, who has said he will not fight the next General Election as leader.

"I think that Tony will go on until he has said he will stand down, the same will happen with John Prescott and then there will be a fresh leadership election and then we'll go to where we want to be."

Health Secretary Patricia Hewitt also refused to rule herself out from any future bid, saying talk of individual candidates was "premature".

She said Mr Prescott did "an absolutely superb job dealing with some of the most difficult issues right across Government".

And she denied Mr Prescott's affair had lost him public respect.

Ms Hewitt, also said she would be "delighted" if the next deputy leader was a woman.

Constitutional Affairs Minister Harriet Harman - another expected to challenge for the job - said a female deputy next time was a "necessity".

But she has suggested two posts could be created - at least one of which should be a woman.